PSI - Issue 2_B

P. Ferro et al. / Procedia Structural Integrity 2 (2016) 3467–3474

3472

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6

Author name / Structural Integrity Procedia 00 (2016) 000–000

(6)

where K I res is the R-NSIF which characterizes the residual stress field. R m and R correspond to the local load ratio of the nominal applied and real cycle experienced, respectively. Starting from Eqs (4-6), for R = 0, the following equation is obtained (full analytical details are published in Ferro (2014)): �� � � � � � �� � � � � � � � � � ��� � ��� � � � ��� � � � � ��� � � � ��� � (7) where  n (=  n,max ) is the nominal stress amplitude. Similarly, for R>0 the following relationship is obtained: � �� �� � ��� � ��� � � � ���� � � ���� � � � � � � � � � ��� � ��� � � � ��� � ���� � � � � � ��� � � � ��� � ���� � � (8) where C is a constant and z is the slope of the fatigue data expressed in terms of local strain energy density experimentally calculated ( , subscripts D 1 and D 2 indicate two points of the curve ); k I is a non-dimensional coefficient, analogous to the shape functions of cracked components calculated using the following equation: � �� � � � � � � ��� � (9) where  n is the remotely applied stress, and t is a geometrical parameter of the plate, according to Lazzarin and Tovo (1998). Eqs. (7) and (8) are applied in high-cycle fatigue regime where the redistribution of the pre-existing residual stresses is considered negligible (Ferro (2014)). z  Log N D 1 / N D 2   / Log  W D 2 /  W D 1    W ( N )

Fig. 5. Residual stress influence on fatigue strength of the AA 6063 butt-welded joint predicted by Eq. (7) (Ferro et al. (2016))

This model was validated using experimental results obtained for the fatigue strength of butt-welded AA 6063